Correct. The easiest way to find the maximum height is to find the vertex of the parabola that this equation represents. Substituting in the initial velocity and height, you have $\displaystyle{h}=-{16}{{t}}^{{2}}+{32}{t}+{15}\usepackage{cmbright}\Huge\$ , rewritten as $\displaystyle{h}=-{16}{\left({{t}}^{{2}}-{2}{t}\right)}+{15}\usepackage{cmbright}\Huge\$ . Generating a perfect square adds -16 to both sides: $\displaystyle{h}+{\left(-{16}{\left({1}\right)}\right)}=-{16}{\left({{t}}^{{2}}-{2}{t}+{1}\right)}+{15}\usepackage{cmbright}\Huge\$ . Now simplifying the equation and solving for h yields $\displaystyle{h}={16}{{\left({t}-{1}\right)}}^{{2}}+{31}\usepackage{cmbright}\Huge\$ . The vertex of the parabola is (1, 31), so the maximum height is 31 feet.